A student is performing an experiment using a resonance column and a tuning fork of frequency `244s^(1-)`. He is told that the air in the tube has been replaced by another gas (assuming that the air column ramains filled with the gas). If the minimum height at which resonace occurs is `(0.350+- 0.005)m`, the gas in the tube is (Useful information : `sqrt(167RT) = 640J^(1//2)mode^(-1//2)`,
`sqrt(140RT) = 590J^(-1//2)`. the molar masses `M` in grams are given in the options. take the values of `sqrt((10)/(M))` for each gas as given there.)

Options

A. (a) `Neon (M = 20, sqrt((10)/(20)) = (7)/(10))`
B. (b) `Nitrogen (M = 28, sqrt((10)/(28)) = (3)/(5))`
C. ( c ) `Oxygen (M = 32, sqrt((10)/(32)) = (9)/(16))`
D. (d) `Argon (M = 36, sqrt((10)/(36)) = (17)/(32))`

Answer

D

Explanation

(d) Here, `v = (v)/(4l) = sqrt((gammaRT)/(M xx 10^(-3)))xx (1)/(4l) rArr v = v xx 4l`
rArr `v = 336.7m//s to 346.5m//s`
For monatomic gas `gamma = 1.67`
`v = sqrt((gammaRT)/(M xx 10^(-3))) = sqrt(100gammaRT) xx sqrt((10)/(M)`
`= sqrt(167RT) xx sqrt((10)/(M)) = 640sqrt((10)/(M)`
For Neon `M = 20` and `sqrt((10)/(20)) = (7)/(10)`
:. `v = 640 xx (7)/(10) = 448ms^(-1)`
:. `(a)` is incorrect
For Argon `M = 36`, `sqrt((10)/(36)) = (17)/(32)`
:. `v = 640 xx (17)/32) = 340ms^(-1)`
:. `(d)` is the correct option.
For diatomic gas `gamma = 1.4`
`v = sqrt(140RT)sqrt((10)/(M)) = 590 xx sqrt((10)/(M))`
For Oxygen `sqrt((10)/(32)) = (9)/(16)`
:. `v = 590 xx (9)/(16) = 331.87ms^(-1)`
:. `( c )` is incorrct
For Nitrigen `sqrt((10)/(28)) = (3)/(5)`
:. `v = 590 xx (3)/(5) = 354 ms^(-1)`
:. `(b)` is incorrct